Accession Number:

ADA446729

Title:

Global Attractor for Damped Abstract Nonlinear Hyperbolic Systems

Descriptive Note:

Corporate Author:

NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION

Personal Author(s):

Report Date:

1998-01-01

Pagination or Media Count:

24.0

Abstract:

This work is concerned with the long time dynamics of a class of abstract nonlinear second order in time systems with damping. This class of systems describes nonlinear dissipative elastic models with the nonlinear term produced by neo-Hookean type stress-strain relationships. In our earlier paper it was shown that these systems give rise to a weak dynamical system and that there exists a weak compact attractor. In the present work, using a somewhat more detailed analysis based in part on the results of H.T. Banks, D.S. Gilliam and V.I. Shubov on the existence and uniqueness of the weak solutions, we show that these systems generate a strong dynamical system also. More importantly, we are able to prove the existence of a compact strong global attractor. Finally, we make several comments concerning the regularity of this attractor, and present two examples.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE